## TPMS

TPMS is the acronym of Tire Pressure Monitoring System, and nowadays is widely used in production cars. How does this system work? How many types exist?

## Tires pressure and handling

Before talking about the system we need to understand why is important monitoring tire pressure. The answer seems to be simple, the reason is security. But from which phenomena does security depend?

Starting from a reference condition, the contact patch of tire with an excessive inflation pressure is reduced. In this condition main effects are a reduced grip and an irregular tire wear, more in the center and less on the external surface. Due to the increased tire vertical stiffness the ride comfort is worse. Furthermore, the steering wheel is “lighter” due to the reduced self-aligning moment of the tire, i.e. the moment created by the tire lateral force that in normal conditions is in opposition to the steering moment.

At the opposite a too low tire pressure leads anyway to a reduced contact patch and an irregular tire wear, more on the outer and less in the center. Vertical stiffness is reduced because vertical stiffness is lower, but at the same time strain amplitude is increased and more heat is generated inside the tire, increasing the possibility to damage.

In both cases tire cornering stiffness changes, in this last case decreases, so tire tends to generate less lateral force.

## Tire deflation

Pressure can be lost mainly in two ways:

• Tire damage or valve failure: this two cases lead to a fast deflation, and are the most dangerous;
• Air diffusion: it consists in air leakage through tire compound due to its permeability. It is a slow process, but for this reason car manufacturers advice to check tire pressure regularly. In order to reduce air diffusion, tire manufacturers introduce on the inner part of the compound a special layer, called inner layer, with a low permeability.

## Types of TPMS

There are two types of systems: direct and indirect. The main differences are the measurement accuracy and the cost, higher for the first one.

### 1. Direct system

Is a stand-alone system. Is composed by pressure (and sometime also temperature) sensors mounted instead of normal inflation valves that send the informations as a signal to one or more antennas. The last ones send the signal to the Electronic Control Unit and are processed.

This kind of TPMS is able to measure not only id the tire pressure is too high or too low, but indicates which wheel is affected to the problem and shows the values of pressure and temperature for every tire.

The software used to process the signals must take in account all the different conditions in which tire pressure varies but falls in the normal range, for example the increased or reduced vertical load on the tire  due to load transfer on braking or turning.

In order to have always the correct reference pressure, the system bust be initialized correctly. When tire pressure is changed manually, or when tires are changed, the reset button must be used. From this moment learning phase starts: sensors start to record the pressure, using that values as reference. Being a very sensitive system it should be initialized correctly to avoid false alarms.

Among advantages there are of course measurement accuracy and the possibility to read pressure and temperature values.

Some weaknesses are the higher cost of the system than the indirect one due to necessity to design a stand-alone system; the possibility of failure of one or more sensor and the presence of a battery with its own life cycle.

### 2. Indirect system

This TPMS does not need additional components but are used speed sensors already mounted on the wheels and used by ABS system.

This is the first advantage, i.e. a cheaper system because no additional components must be installed, programmed and calibrated. The disadvantage can be found on the title of the paragraph: because it is an indirect system, tire pressure is not measured but estimated…even better the difference between a reverence value and a limit one is estimated.

### How does it work?

Let’s imagine that we are driving our car with all four wheel with the same size on a straight line, If tires have the same pressure the linear speed of each of them, calculated as product between angular velocity $\omega$ and rolling radius, must be equal to the other ones and to the vehicle one. If one tire is deflated, to reach the same linear speed of the vehicle it must increase its $\omega$. The system measure this change due to the reduced rolling radius and a warning appears on the dashboard.

As usual the real principle is not simple as explained. The dimension of rolling radius i modified by many factors, some of which are:

• Longitudinal and lateral load transfers;
• A different load distribution on the four wheels, for example because we are living for the holidays and our car is full of bags;
• Just driving on a turn, because the four wheels have a different angular speed;
• On high speed, because the tire is deformed on a radial way;
• Different wear between one tire and one other.

All this factors must be evaluated by ECU.

Every time that we change tires, also this system must be correctly initialized at the new reference pressures.

One more disadvantage is that the warning message is very generic, no value is displayed, nor in which wheel there is the problem. Just a warning light is displayed, like in the following image.

Some indirect TPMS are able to estimate the pressure reduction caused by air diffusion. Through frequency analysis of belt oscillations, linked to inflation pressure, are able to notice the problem and a warning alarm is displayed.

[latexpage]